+1. Interesting to note that both of us had similar kind of sketch of the function in our mind.
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user17762Jan 14 '13 at 3:33

@Marvis Seems the easiest to use. I wanted a 'simple' example, though OP should have seen Logistic functions under exponentials too. Just wondering, are you an analyst? Your 'calculus/analysis' proofs are very beautiful.
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Calvin LinJan 14 '13 at 4:34

Thanks and the answer to your question is "I don't know" :-). I am a doctoral student in computational mathematics working in numerical linear algebra/ algorithms. I just dabble in different areas of math with courses I have taken.
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user17762Jan 14 '13 at 4:49

And brilliant.org looks like a great initiative! Good one. Is there a way I can contribute to it?
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user17762Jan 14 '13 at 7:45

1

Sure. I am also interested in Olympiad/Putnam type problem solving in general. Anyway, in case you guys plan to expand and need someone to contribute some time down the line, do keep me posted. :-)
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user17762Jan 18 '13 at 0:52

Inverse function itself may not exist. For example the function $f(x) = \frac{1}{1+e^x}$ is defined from $\mathbb{R}$ to $\mathbb{R}$ which is one to one and bounded. But its inverse $\log\left(\frac{1}{y} -1\right)$ is not defined for all real numbers.